Method and a device for adjusting the transmission power of signals transferred by plural mobile terminals

ABSTRACT

A method for adjusting transmission power, in a wireless cellular telecommunication network, of signals transferred by plural mobile terminals through a wireless interface, the mobile terminals being served by at least one base station or by home base stations, the home base stations being located in the cell of the at least one base station. The method includes: obtaining at least the path gains between the mobile terminals and the at least one base station and at least one home base station; determining statistics from the obtained path gains; obtaining at least one coefficient of a function according to at least a part of the statistics; transferring an information representative of the at least one obtained coefficient to the mobile terminals.

The present invention relates generally to a method and a device foradjusting the transmission power, in a wireless cellulartelecommunication network, of signals transferred by plural mobileterminals through a wireless interface.

Wireless cellular telecommunication networks are largely deployed butthere are still some areas not covered by the base stations of thewireless cellular telecommunication network. The base stations aredeployed by an operator according to a given planning.

For example, the access to the wireless cellular telecommunicationnetwork might not be possible or might require a too high transmissionpower or a too low spectral efficiency, i.e., too many system resourcesfor a mobile terminal located in a building, if the signals radiated bythe base stations and/or by the mobile terminal are too attenuated.

Solutions are proposed today. Particular base stations which are notnecessarily deployed by an operator and thus not following a givenplanning, like home base stations or femto base stations or pico basestations or relays, may provide coverage areas within the buildings andbase station offload. Relays may also provide outdoor coverageextension.

The home base stations or femto base stations provide a limited coveragearea. Due to the constant coverage area size reduction and spectralefficiency increase, the inter-cell interference has become a mainissue. Inter-cell interference coordination (ICIC) techniques intend tomitigate the inter-cell interference problem. Classically, a mobileterminal reports to the base station the mobile terminal is currentlyserved by, the interference it receives from neighbouring base stationsand/or home base stations. Base stations exchange also messages betweeneach other in order to allow an efficient ICIC. However, the basestation to base station messages need establishment of links between thebase stations. The same links between base stations and home basestations or between home base stations cannot be established in somecases.

A massive deployment of home base stations prevents from having suchlinks between a base station and all the home base stations locatedwithin the coverage area of the base station. Even if the links exist,the amount of messages on these links must be as low as possible inorder not to put an excessive burden on the core network. These homebase stations may strongly interfere with the base station and evencreate coverage holes.

Without shadowing, the interference impact depends on the distanceseparating the base station and the home base station. In the uplinkchannel, the lower the distance between a base station and a home basestation is, the higher the interference generated by mobile terminalsserved by the home base station on all mobile terminals served by thebase station is. In the uplink channel, with power control, the higherthe distance between a base station and a home base station is, thehigher the interference created by mobile terminals served by the basestation on all mobile terminals served by the home base station is.

With shadowing, the interference impact is not only related to thedistance between the home base station and the base station. In uplinkchannel, the interference also depends on the shadowing between eachmobile terminal served by a home base station and the base station.Thus, the higher the average path-gain between mobile terminals servedby a home base station and the base station is, the higher theinterference created by mobile terminals served by the home base stationon all mobile terminals served by the base station is. Besides, mobileterminals served by the base station also interfere on the mobileterminals served by a home base station. With path-gain dependent powercontrol, the lower the average path-gain between the base station andmobile terminals served by the base station at the neighbourhood of ahome base station is, the higher the interference created by the mobileterminals served by the base station on all mobile terminals served bythe home base station is.

The home base stations may enable a limited number of mobile terminalsto access the wireless cellular telecommunication network through theirrespective resources. The mobile terminals allowed to access theresources of the network through the home base station may be determinedby the owner of the home base station, the network or a combination ofboth.

The owner must be understood here in the general sense: the owner mayonly be the main user of the home base station, the owner may be theperson who rents the home base station or the owner may be the personwho accommodates the home base station in his house or office.

For example, only mobile terminals of the owner of the home base stationand his family can access the wireless cellular telecommunicationnetwork through the home base station. These mobile terminals areassociated with the home base station.

Base stations enable a large number of mobile terminals to access thewireless cellular telecommunication network through their respectiveresources. The mobile terminals allowed to access the resources of thenetwork through the base station may be determined by the operator ofthe wireless cellular telecommunication network.

The cell of a base station is usually much larger than a cell of a homebase station.

Inter-cell interference coordination (ICIC) techniques have beenextensively discussed between base stations.

The present invention aims at avoiding that signals transferred betweenmobile terminals served by home base stations and the home base stationsinterfere on signals transferred between mobile terminals served by basestations and the base stations.

The present invention aims also at avoiding that signals transferredbetween mobile terminals served by base stations and the base stationsinterfere on signals transferred between mobile terminals served by homebase stations and the home base stations.

To that end, the present invention concerns a method for adjusting thetransmission power, in a wireless cellular telecommunication network, ofsignals transferred by plural mobile terminals through a wirelessinterface, the mobile terminals being served by at least one basestation or by home base stations, the home base stations being locatedin the cell of the at least one base station, characterised in that themethod comprises the steps of:

-   -   obtaining the path gains between the mobile terminals and the at        least one base station and the path gains between the mobile        terminals and at least one home base station, and/or noise        measured at the at least one base station and/or at the home        base stations,    -   determining statistics from the obtained path gains and/or        noise,    -   obtaining at least one coefficient of a function according to at        least a part of the statistics determined from the obtained path        gains and/or noise,    -   transferring an information representative of the at least one        obtained coefficient to the mobile terminals in order to enable        the mobile terminals to transfer signals at a transmission power        derived from information representative of the at least one        obtained coefficient.

The present invention concerns also a system for adjusting thetransmission power, in a wireless cellular telecommunication network, ofsignals transferred by plural mobile terminals through a wirelessinterface, the mobile terminals being served by at least one basestation or by home base stations, the home base stations being locatedin the cell of the at least one base station, characterised in that thesystem comprises:

-   -   means for obtaining the path gains between the mobile terminals        and the at least one base station and the path gains between the        mobile terminals and the home base stations and/or noise        measured at the at least one base station and/or at the home        base stations,    -   means for determining statistics from the obtained path gains        and/or noise,    -   means for obtaining at least one coefficient of a function        according to at least a part of the statistics determined from        the obtained path gains and/or noise,    -   means for transferring an information representative of the at        least one obtained coefficient to the mobile terminals in order        to enable the mobile terminals to transfer signals at a        transmission power derived from information representative of        the at least one obtained coefficient.

Thus, the interference of signals transferred between mobile terminalsserved by home base stations and home base stations on signalstransferred between mobile terminals served by base stations and thebase stations is controlled.

Furthermore, the interference of signals transferred between mobileterminals served by base stations and base stations on signalstransferred between mobile terminals served by home base stations andthe home base stations is controlled.

Finally, the noise level at each base station or home base station maybe considered in order to achieve a more efficient optimisation of theperformance of mobile terminals served by the at least one base stationor the home base stations.

According to a particular feature, for mobile terminals served by the atleast one base station, the path gains between the mobile terminals andhome base stations located in the cell of the at least one base stationwhich serves the mobile terminals are obtained and for mobile terminalsserved by home base stations, each path gain between a mobile terminaland only the home base station serving the mobile terminal is obtained.

Thus, the interference of all home base stations HBS is controlled, alsoaccording to the quality of the link between each mobile terminal andits serving home base station or base station. The interference ofmobile terminals MT served by a home base station on another home basestation is not considered in order to avoid a too large complexity.

According to a particular feature, the function is defined for acontinuous range of real values or a plurality of coefficients areobtained, the coefficients being entries of a table representing thefunction.

Thus, a good complexity/performance trade-off can be chosen. Theoptimisation of a function defined for a continuous range of real valuesis easier to achieve whereas tables representing a function may providea better performance.

According to a particular feature, each path gain is a path gain betweenone home base station serving one mobile terminal and said mobileterminal or the path gain between one base station serving one mobileterminal and said mobile terminal or the path gain between one home basestation not serving one mobile terminal and said mobile terminal or thepath gain between one base station not serving one mobile terminal andsaid mobile terminal.

Thus, the path gains for both useful signals and interfering signals areconsidered in order to achieve a more efficient optimisation.

According to a particular feature, a set of at least one coefficient ofthe function is determined for each home base station and for the atleast one base station.

Thus, a case-by-case power control, for each home base station or basestation is applied in order to take into account the home base stationor base station environment.

According to a particular feature, a same set of at least onecoefficient is determined for all the home base stations.

Thus, a common power control is applied to all home bases stations inorder to reduce the signalling amount in the network and theoptimisation complexity.

According to a particular feature, the path gains are obtained by thehome base stations and the at least one base station and statistics aredetermined by the home base stations and the at least one base station.

Thus, signalling is reduced in the network since the home base stationsand the at least one base station only transfer statistics common to allmobile terminals they serve or they have served instead of transferringone particular data per mobile terminal.

According to a particular feature, the at least one coefficient of thefunction is obtained by the base station or by a server of the wirelesscellular telecommunication network.

Thus, the at least one coefficient of the function is obtained in acentralised manner, which achieves a better performance.

According to a particular feature, information representative of the atleast one obtained coefficient is transferred to each mobile terminalvia the base station serving the mobile terminal or via the home basestation serving the mobile terminal.

Thus, even if the at least one coefficient of the function is optimisedbased on statistics on many mobile terminals and is specific to a homebase station or base station or even common to many home base stations,the transmit power for each mobile terminal still depends on someparameters which are specific to the mobile terminal, like for instancethe path gain between the mobile terminal and its serving base stationor home base station. Thus, mobile terminal specific transmission poweris applied, which achieves a better performance.

According to a particular feature, when the at least one coefficient ofthe function is obtained by the server, the at least one base stationtransfers to the server the harmonic mean of noise measured at the atleast one base station and/or the mean of noise measured at the at leastone base station and/or the mean over all mobile terminals served orhaving been served by the at least one base station of ratios of thepath gain between a mobile terminal and a home base station over thepath gain between the mobile terminal and its serving base station.

Thus, thanks to this reduced signalling through the network between thebase station and the server, different types of power control, specificto each home base station or common to many home base stations, with apower control function depending on a single path gain or on a couple ofpath gain or with a power control function being a look-up table can beapplied.

According to a particular feature, each home base station transfers tothe base station in the cell of which the home base station is locatedor to the server, the mean over all mobile terminals served or havingbeen served by the home base station of ratio of the path gain between amobile terminal served by a home base station and the base station overthe path gain between the mobile terminal served by a home base stationand the home base station and/or the harmonic mean of noise measured atthe home base station and/or the mean of the noise measured at the homebase station and/or the mean over all mobile terminals served or havingbeen served by the home base station of the path gain between a mobileterminal served by a home base station and the base station and/or thestandard deviation over all mobile terminals served or having beenserved by the home base station of the path gain between a mobileterminal served by a home base station and the base station and/or theload of the home base station and/or the harmonic mean over all mobileterminals served or having been served by the home base station of thepath gain between a mobile terminal served by a home base station andthe home base station, the mean over all mobile terminals served orhaving been served by the home base station of the path gain between amobile terminal served by the home base station and the home basestation and/or the standard deviation over all mobile terminals servedor having been served by the home base station of the path gain betweena mobile terminal served by the home base station and the home basestation.

Thus, thanks to this reduced signalling through the network between thehome base station and the base station in the cell of which the homebase station is located, different types of power control, specific toeach home base station or common to many home base stations, with apower control function depending on a single path gain or on a couple ofpath gain or with a power control function being a look-up table can beapplied.

According to still another aspect, the present invention concernscomputer programs which can be directly loadable into a programmabledevice, comprising instructions or portions of code for implementing thesteps of the method according to the invention, when said computerprograms are executed on a programmable device. Since the features andadvantages relating to the computer programs are the same as those setout above related to the method and device according to the invention,they will not be repeated here.

The characteristics of the invention will emerge more clearly from areading of the following description of example embodiments, the saiddescription being produced with reference to the accompanying drawings,among which:

FIG. 1 represents a wireless cellular telecommunication network in whichthe present invention is implemented;

FIG. 2 is a diagram representing the architecture of a base station inwhich the present invention is implemented;

FIG. 3 is a diagram representing the architecture of a home base stationin which the present invention is implemented;

FIG. 4 is a diagram representing the architecture of a server in whichthe present invention is implemented;

FIG. 5 discloses an algorithm executed by each home base station andeach base station according to the present invention;

FIG. 6 discloses an algorithm executed by each base station or theserver according to the present invention;

FIG. 7 discloses an algorithm executed by each home base station andeach base station according to the present invention.

FIG. 1 represents a wireless cellular telecommunication network in whichthe present invention is implemented.

In FIG. 1, two base stations BS1 and BS2 and plural home base stationsHBS1 to HBS4 of a wireless cellular telecommunication network are shown.

Only two base stations BS1 and BS2 and four home base stations HBS1 toHBS4 are shown but we can understand that the present invention workswhen a more important number of base stations BS and/or home basestations HBS exist.

The base stations BS1 and BS2 are for example base stations of awireless cellular telecommunication network which serve mobile terminalslocated in the cell CE1 of the base station BS1 and/or in the cell CE2of the base station BS2.

Only three mobile terminals MT1, MT2 and MT3 are shown in FIG. 1 for thesake of clarity.

The home base stations HBS1 to HBS4 are named also femto base stationsor pico base stations or relays.

For example, a relay is a home base station HBS which is connected tothe wireless cellular telecommunication network via a wireless link withthe base station BS1 or BS2.

Each home base station HBS1 to HBS4 is for example located into home andmay enable mobile terminals MT associated to the home base station HBSto access the wireless cellular telecommunication network.

For example, the home base stations HBS1 and HBS4 are located in thesame building.

For example, a home base station HBS and a mobile terminal MT areassociated when the home base station HBS belongs to the owner of themobile terminal MT or when the home base station HBS belongs to thefamily or friends of the owner of the mobile terminal MT.

When a mobile terminal MT is served by a base station BS or a home basestation HBS, it can receive or establish or continue a communicationwith a remote telecommunication device through the base station BS orthe home base station HBS.

The base station BS1 is able to receive signals transferred by mobileterminals MT1, MT2 and MT3 which are located in the area or cell CE1.The base station BS1 transfers signals which can be received andprocessed by mobile terminals MT1, MT2 and MT3 located in the cell CE1.The base station BS2 is able to receive signals transferred by mobileterminals MT2 and MT3 which are located in the area or cell CE2. Thebase station BS2 transfers signals which can be received and processedby mobile terminals MT2 and MT3 located in the cell CE2.

In the example of FIG. 1, the base stations BS1 and BS2 have only onerespective cell CE1 and CE2. The present invention is also applicablewhen the base stations BS have plural cells. In that case, the presentinvention is applied independently for each cell of the base stationsBS.

The home base stations HBS1 to HBS4 are comprised in the cell CE1 of thebase station BS1. The home base station HBS3 is also comprised in thecell CE2 of the base station BS2.

The home base stations HBS1 to HBS4 radiate signals which can bereceived and processed by mobile terminals MT1 and MT2 in theirrespective cell.

The home base station HBS1 is able to receive signals transferred by themobile terminal MT1 which is located in the area or cell CEHB1. The homebase station HBS1 transfers signals which can be received and processedby the mobile terminal MT1 located in the cell CEHB1.

The home base station HBS3 is able to receive signals transferred by themobile terminal MT2 which is located in the area or cell CEHB3. The homebase station HBS3 transfers signals which can be received and processedby the mobile terminal MT2 located in the cell CEHB3.

The area CEHB2 is the cell of the home base station HBS2. The area CEHB4is the cell of the home base station HBS4.

The mobile terminal MT3 is served by the base station BS1. The signalstransferred by mobile terminals MT1 and MT2 and served by the home basestation HBS1 and HBS3, respectively, interfere on signals transferred bythe mobile terminal MT3 and received by the base station BS1. The mobileterminal MT2 is served by the home base station HBS3. The signalstransferred by mobile terminal MT3 and served by the base station BS1interfere on signals transferred by the mobile terminal MT2 and receivedby the base station HBS3.

In FIG. 1, a server Serv is shown. The server Serv is a core networkdevice that may control plural cells of plural base stations BS and mayexecute the present algorithm instead of the base station BS. The serverServ may also be named a coordinator.

According to the invention, the base station BS performs in combinationwith home base stations HBS or the server Serv performs in combinationwith at least one base station BS and home base stations HBS inter cellinterference coordination procedure by:

-   -   obtaining the path gains between the mobile terminals MT and the        at least one base station BS and the path gains between the        mobile terminals MT and at least one home base station HBS,        and/or noise measured at the at least one base station BS and/or        at the home base stations HBS,    -   determining statistics from the obtained path gains and/or noise        measured at the at least one base station BS and/or at the home        base stations HBS,    -   obtaining at least one coefficient of a function according to at        least a part of the statistics determined from the obtained path        gains,    -   transferring an information representative of the at least one        obtained coefficient to the mobile terminals MT in order to        enable the mobile terminals MT to transfer signals at a        transmission power derived from information representative of        the at least one obtained coefficient.

According to the invention, the transmit power of the mobile terminalsMT1 and MT2 served by a home base station HBS and the transmit power ofthe at least one mobile terminal MT3 served by a base station BS is setin order to optimize the link conditions between mobile terminals servedby a home base station HBS and the home base station HBS and linkconditions between mobile terminals served by a base station BS and thebase station BS.

According to the particular example of FIG. 1, the link conditions arethe Signal to Interference plus Noise Ratios (SINR) of mobile terminalsMT1 and MT2 served by a home base station HBS and at least the mobileterminal MT3 served by a base station BS.

According to the invention, each mobile terminal MT served by a basestation BS reports the path gain between itself and the base station BSit is served by and/or the path gain between itself and at least onebase station BS which serves interfering mobile terminals and/or thepath gain between itself and home base stations HBS.

An interfering mobile terminal MT is a mobile terminal MT which radiatessignals which interfere at least one base station BS or at least onehome base station HBS which does not serve said interfering mobileterminal MT.

Each mobile terminal MT served by a home base station HBS reports thepath gain between itself and the home base station HBS it is served byand/or between itself and at least one base station BS which servesinterfering mobile terminals.

Each base station BS builds statistics from the path gains reportstransferred by each mobile terminal MT served and/or which have beenserved by said base station BS. The statistics may be transferred to theserver Serv.

In a variant, each base station BS also builds statistics on the noiselevel it receives. The statistics may be transferred to the server Serv.

Each home base station HBS builds statistics from the path gains reportstransferred by each mobile terminal MT served and/or which have beenserved by said home base station HBS. The statistics are transferred tothe base station BS the cell CE of which the home base station HBS islocated in or to the server Serv.

In a variant, each home base station HBS also builds statistics on thepath gain between itself and the base station BS the cell CE of whichthe home base station HBS is located in.

In a variant, each home base station HBS also builds statistics on thenoise level it receives. The statistics may be transferred to the serverServ or to a base station BS.

Statistics may be transferred periodically, each hour or on a day basis.

The base station BS optimizes the power control rule for all mobileterminals MT served by a home base station HBS located in the cell CE ofthe base station BS and according to particular examples for the mobileterminals MT served by the base station BS.

Alternatively, the server Serv optimizes the power control rule for allmobile terminals MT served by a home base station HBS located in thecell of a base station BS the server Serv is in charge of and for allthe mobile terminals MT served by the base stations BS the server Servis in charge of.

According to the invention, the power control rule is a function f ofthe pair useful path gain, interfering path gains wherein the usefulpath gain is the path gain between a mobile terminal MT and its servinghome base station HBS or its serving base station BS. An interferingpath gain is a path gain between an interfering mobile terminal MT and abase station BS which does not serve said interfering mobile terminal MTor is a path gain between an interfering mobile terminal MT and a homebase station HBS which does not serve said interfering mobile terminalMT. The home base station HBS is located in the cell CE of the basestation BS or close to the cell CE of the base station BS.Alternatively, the power control rule is a function f of a pair ofuseful link quality and interfering link quality. For instance a usefullink quality is a ratio of useful path gain over noise.

Each home base station HBS receives the power control rule which is thefunction f, analytically defined or defined as a look-up table and thecoefficients and transfers the power control rule and the coefficientsor the transmission power to be used by each mobile terminal MT to eachmobile terminal MT the home base station HBS serves.

In a variant, each home base station HBS receives the coefficients ofthe power control rule and transfers to the mobile terminal MT, thepower control rule and the coefficients or the coefficients or thetransmission power to be used by each mobile terminal MT to each mobileterminal MT the home base station HBS serves. The coefficients of thepower control rule may be entries of a table representing the function,i.e. a look up table.

Each base station BS may receive the power control rule which is thefunction f, analytically defined or defined as a look-up table and thecoefficients and transfers the power control rule and the coefficientsor the transmission power to be used by each mobile terminal MT to eachmobile terminal MT the base station BS serves.

In a variant, each base station BS may receive the coefficients of thepower control rule and transfers to the mobile terminal MT, the powercontrol rule and the coefficients or the coefficients or thetransmission power to be used by each mobile terminal MT to each mobileterminal MT the base station BS serves. The coefficients of the powercontrol rule may be entries of a table representing the function, i.e. alook up table.

The power optimisation is for example executed as it will be disclosedhereinafter.

For example, the power control optimisation is done by choosing astructure which may be analytical or under the form of a look-up tablefor the function f and by choosing the best function or functioncoefficient or coefficients which define a given function for optimisinga given criterion. The optimisation may be analytical or numerical i.e.by testing many functions or coefficient sets and keeping the best one.

The numerical/analytical optimisation may be done with a given structurefor the power setting function f, e.g., affine in dB and/or within agiven range between f_(min) and f_(max). For instance, if f(x)=a·x+b,the coefficients a and b of the function f are optimised.

For instance, when using look-up tables, function f depending onvariable x, which might be a vector of variables, is described byquantifying x to a given set of discrete values. For instance, eachdimension of x is quantified by choosing a quantification range[x_(min), x_(max)] and a quantification step. The global optimisationresults in choosing the best look-up table, i.e., the best value of ffor each discrete value of x, according to the criterion to optimise.

The optimisation criterion may be a quantile or mean of a given randomvalue if there is a single random value to take into account or afunction of several random values like a sum of quantiles, sum of means,quantiles of quantiles, quantiles of means, quantile on all randomvalues.

The given random value may be specific to all the mobile terminals MTserved by the same home base station HBS or the same base station BS incase of a single random value. For instance, the optimisation couldensure that the degradations brought on a base station BS by all themobile terminals MT served by all home base stations HBS located in thecell CE of the base station BS and by the mobile terminals MT served bythe base station BS on each home base station HBS located in the cell CEof the base station BS are the same.

For example, in order to perform this optimisation, a random value maybe the ratio of the signal SINR without interference over SINR withinterference. For example, a random value in order to perform thisoptimisation may be the ratio of Shannon capacity without interferenceover Shannon capacity with interference.

These ratios depend on function f. Interference means the signalstransferred by a mobile terminal MT served by a base station BS or ahome base station HBS which interferes or reduces capacity on uplinksignals received by another base station BS or another home base stationHBS not serving said mobile terminal MT.

Uplink signals are signals received by a home base station HBS or a basestation BS from a mobile terminal MT served by said home base stationHBS or said base station BS.

Uplink signals are not signals received by a home base station HBS or abase station BS from a mobile terminal MT not served by said home basestation HBS or said base station BS.

The given random value may be global for all the mobile terminals MTserved by all home base stations HBS located in a cell CE of at leastone base station BS.

For instance, the optimisation could ensure that the degradation broughtby all the mobile terminals MT served by all the home base stations HBSlocated in a cell CE of a base station BS on uplink signals received bythe base station BS is set with respect to the degradation brought bythe mobile terminals MT served by the base station BS on all the uplinksignals received by the home base stations HBS located in the cell ofthe base station BS.

For instance, the degradation brought by the base station BS on theuplink signals received by the home base stations HBS is the meandegradation brought by the mobile terminals MT served by the basestation BS on all the uplink signals received by all the home basestations HBS located in the cell of the base station BS.

For example, a random value in order to perform this optimisation may bethe ratio of the signal SINR without interference over SINR withinterference. For example, a random value in order to perform thisoptimisation may be the ratio of Shannon capacity without interferenceover Shannon capacity with interference. These ratio may depend onfunction f. Interference means base station BS uplink signalsinterference or capacity reduction on uplink signals received by eachhome base station HBS and means interference or capacity reduction ofall the home base stations HBS located in the cell CE of a base stationBS on the uplink signals received by the base station BS.

In another example, the optimisation could ensure that the degradationbrought by all the mobile terminals MT served by a home base station HBSlocated in a cell CE of a base station BS on the base station BSperformance is set to a given value and ensure that the performance ofthe home base stations HBS is maximised.

According to the invention, statistics reported from the base stationsBS and home base stations HBS may be quantized, e.g. using a basis ofpredetermined functions or the mean and/or variance of a givendistribution like a Gaussian distribution of a random variable which maybe expressed in decibels (dB) and/or histograms. Generally, thanks tothe high variance of the shadowing compared to the distance-dependentpropagation loss distribution variance, the Gaussian distribution is agood solution for path gains in dB.

FIG. 2 is a diagram representing the architecture of a base station inwhich the present invention is implemented.

The base station BS has, for example, an architecture based oncomponents connected together by a bus 201 and a processor 200controlled by the programs as disclosed in FIGS. 5, 6 and 7.

The bus 201 links the processor 200 to a read only memory ROM 202, arandom access memory RAM 203, a wireless interface 205 and a networkinterface 206.

The memory 203 contains registers intended to receive variables and theinstructions of the programs related to the algorithms as disclosed inFIGS. 5, 6 and 7.

The processor 200 controls the operation of the network interface 206and of the wireless interface 205.

The read only memory 202 contains instructions of the programs relatedto the algorithms as disclosed in FIGS. 5, 6 and 7, which aretransferred, when the base station BS is powered on, to the randomaccess memory 203.

The base station BS may be connected to a telecommunication networkthrough the network interface 206. For example, the network interface206 is a DSL (Digital Subscriber Line) modem, or an ISDN (IntegratedServices Digital Network) interface, etc. Through the network interface206, the base station BS may transfer messages to the core network ofthe wireless cellular telecommunication network.

The wireless interface 205 and the network interface 206 are theresources of the base station BS used by a mobile terminal in order toaccess to the wireless cellular telecommunication network when themobile terminal establishes or receives a communication with a remotetelecommunication device.

FIG. 3 is a diagram representing the architecture of a home base stationin which the present invention is implemented.

The home base station HBS has, for example, an architecture based oncomponents connected together by a bus 301 and a processor 300controlled by the programs as disclosed in FIGS. 5 and 7.

The bus 301 links the processor 300 to a read only memory ROM 302, arandom access memory RAM 303, a wireless interface 305 and a networkinterface 306.

The memory 303 contains registers intended to receive variables and theinstructions of the programs related to the algorithms as disclosed inFIGS. 5 and 7.

The processor 300 controls the operation of the network interface 306and of the wireless interface 305.

The read only memory 302 contains instructions of the program related tothe algorithms as disclosed in FIGS. 5 and 7, which are transferred,when the home base station HBS is powered on, to the random accessmemory 303.

The home base station HBS may be connected to a telecommunicationnetwork through the network interface 306. For example, the networkinterface 306 is a DSL (Digital Subscriber Line) modem, or an ISDN(Integrated Services Digital Network) interface or a wireless linklinking the home base station HBS to the base station BS, etc. Throughthe network interface 306, the home base station HBS may transfermessages to the core network of the wireless cellular telecommunicationnetwork.

The wireless interface 305 and the network interface 306 are theresources of the home base station HBS used by a mobile terminal inorder to access to the wireless cellular telecommunication network whenthe mobile terminal establishes or receives a communication with aremote telecommunication device.

FIG. 4 is a diagram representing the architecture of a server in whichthe present invention is implemented.

The server Serv has, for example, an architecture based on componentsconnected together by a bus 401 and a processor 400 controlled by theprogram as disclosed in FIG. 6.

The bus 401 links the processor 400 to a read only memory ROM 402, arandom access memory RAM 403 and a network interface 406.

The memory 403 contains registers intended to receive variables and theinstructions of the programs related to the algorithm as disclosed inFIG. 6.

The processor 400 controls the operation of the network interface 406.

The read only memory 402 contains instructions of the program related tothe algorithm as disclosed in FIG. 6, which are transferred, when theserver Serv is powered on, to the random access memory 403.

The server Serv is connected to the telecommunication network throughthe network interface 406. For example, the network interface 406 is aDSL (Digital Subscriber Line) modem, or an ISDN (Integrated ServicesDigital Network) interface, etc. Through the network interface 406, theserver Serv may transfer messages to the core network and/or basestations BS and/or home base stations of the wireless cellulartelecommunication network.

FIG. 5 discloses an algorithm executed by each home base station andeach base station according to the present invention.

More precisely, the present algorithm is executed by the processor 200of each base station BS and by the processor 300 of each home basestation HBS.

At step S500, the processor 200 detects the reception through thewireless interface 205 of measurement reports transferred by mobileterminals MT the base station BS serves.

Each measurement report may comprise the path gain between the servingbase station BS and the mobile terminal MT which transfers the report,the path gain between the mobile terminal MT which transfers the reportand base station BS interfered by the mobile terminal MT which transfersthe report and the path gains between the mobile terminal MT whichtransfers the report and each home base station HBS interfered by themobile terminal MT.

It has to be noted here that different measurement reports may bereceived. Each measurement report may comprise one or several abovementioned information.

The measurement reports may be accumulated during a given period of timelike an hour or like a day.

Each base station BS and each home base station HBS are identified inthe report. It has to be noted here that in a variant, instead of pathgains, the report or reports may include received power measurements. Inthis case, the transmit power by base station BS and by home basestations HBS must be known by the base station BS or the server Serv.

In a similar way, the processor 300 detects the reception through thewireless interface 305 of measurement reports transferred by mobileterminal MT the home base station HBS serves.

Each measurement report may comprise the path gain between the servinghome base station HBS and the mobile terminal MT which transfers thereport, the path gain between the mobile terminal MT which transfers thereport and base station BS interfered by the mobile terminal MT whichtransfers the report and the path gains between the mobile terminal MTwhich transfers the report and each home base station HBS interfered bythe mobile terminal MT.

It has to be noted here that different measurement reports may bereceived. Each measurement report may comprise one or several abovementioned information.

The measurement reports may be accumulated during a given period of timelike an hour or like a day.

Each base station BS and each home base station HBS are identified inthe report. It has to be noted here that in a variant, instead of pathgains, the report may include received power measurements. In this case,the transmit power by base stations BS and by home base stations HBSmust be known by the home base station HBS or the base station BS or theserver Serv.

At next step S501, the processor 200 builds statistics from the receivedreports. The statistics are generally on a long term basis using formerreports received from mobile terminals MT which are no more served bythe base station BS. At the same time the level of additive whiteGaussian noise including thermal noise (AWGN) is obtained from thewireless interface 205.

It has to be noted here that the signals transferred by mobile terminalsMT which are served by another base station BS or another home basestation HBS may be considered as a part of noise level, in addition toadditive white Gaussian noise. This level is named hereinafter AWGN plusinterference level

In a similar way, the processor 300 builds statistics from the receivedreports. The statistics may be built on a long term basis using formerreports received from mobile terminals MT which are no more served bythe base station BS. At the same time AWGN plus interference level, isobtained from the wireless interface 305.

It has to be noted here that the signals transferred by mobile terminalsMT which are served by another base station BS or home base station HBSmay be considered as a part of AWGN plus interference level by the homebase station HBS.

At next step S502, the processor 200 commands the memorizing in the RAMmemory 203 of the built statistics and commands the transfer, throughthe network interface 206, of the built statistics to the server Servwhen the server Serv executes the algorithm which will be disclosed inreference to FIG. 6.

In a similar way, the processor 300 commands the memorizing in the RAMmemory 303 of the built statistics and commands the transfer, throughthe network interface 306, of the built statistics to the server Servwhen the server Serv executes the algorithm of FIG. 6 or to the basestation BS when the base station BS executes the algorithm of FIG. 6.

After that, the algorithm returns to step S500.

FIG. 6 discloses an algorithm executed by each base station or theserver according to the present invention.

More precisely, the present algorithm is executed by the processor 200of the base station BS or by the processor 400 of the server serv.

At step S600, the processor 200 detects the reception through thenetwork interface 206 or through the wireless interface 205 ofstatistics transferred by the home base stations HBS which are locatedin the cell CE of the base station BS.

Alternatively, the processor 400 detects the reception through thenetwork interface 406 of statistics transferred by the home basestations HBS which are located in the cell CE of each base station BSthe server Serv is in charge of. The statistics may be transferred viathe base station BS the cell CE of which home base stations HBS arelocated in.

At step S601, the processor 200 reads from the RAM memory 203 statisticsbuilt at step S501 of FIG. 5.

Alternatively, the processor 400 detects the reception through thenetwork interface 406 of statistics transferred by each base station BSthe server Serv is in charge of.

At next step S602 the processor 200 optimises the power control rule ofthe base station BS and of the home base stations HBS which are locatedin the cell CE of the base station BS.

Alternatively, the processor 400 optimises the power control rule of thebase stations BS it is in charge of and of the home base stations HBSwhich are located in the cells of the base stations BS the server Servis in charge of.

The power control rule optimisation is based on at least one function fdetermination.

According to a first example of realization of the present invention,the function f is specific to each cell CE or CEHB of a base station BSor a home base station HBS. The considered power control inverts thepath gain between a mobile terminal MT served by the base station BS andthe base station BS or the path gain between a mobile terminal MT andthe home base station HBS serving the mobile terminal MT:

${{f\mspace{14mu} G^{U}} = \frac{\beta}{G^{U}}},$

where G^(U) is the useful path gain from the mobile terminals MT and thebase station BS or the home base station HBS serving a mobile terminalMT. β is a scalar value associated to the function and to be optimised.

The resulting power control with this function is for mobile terminalMTj served by a home base station HBSi:

$P_{i,j}^{F} = {{f_{i}^{F}G_{i,j}^{F}} = \frac{\beta_{i}^{F}}{G_{i,j}^{F}}}$

where ( )^(F) denotes the home base station HBS and G_(i,j) ^(F) is thepath gain between the mobile terminal MTj served by the home basestation HBSi and the home base station HBSi.

The resulting power control with this function is for the mobileterminal MTk served by a base station BS

$P_{k}^{M} = {{f^{M}\mspace{14mu} G_{k}^{K}} = \frac{\beta^{M}}{G_{k}^{M}}}$

where ( )^(M) denotes for the base station BS and G_(k) ^(M) is the pathgain between the mobile terminal MTk served by the base station BS andthe base station BS.

The optimisation ensures that the degradation brought by all theinterfering mobile terminals MT served by home base stations HBS on thebase station BS performance and by the mobile terminals MT served by thebase station BS on each home base station HBS performance is the same.

The performance degradation is expressed by a SINR ratio of SINR withoutinterference over SINR with interference. At a base station BS, theratio, denoted SR^(M), is the SINR without interference of interferingmobile terminals MT served by home base station HBS over the SINR withinterference of interfering mobile terminals MT served by home basestation HBS.

At a home base station HBS, the ratio, denoted SR_(i) ^(F), is the SINRwithout interference of interfering mobile terminals MT served by thebase station BS over the SINR with interference of interfering mobileterminals MT served by the base station BS.

With the chosen function f, the ratios are as follows:

${SR}_{i}^{F} = {\frac{{SINR}_{i}^{FwoM}}{{SINR}_{i}^{FwM}} = {\frac{\frac{\beta_{i}^{FwoM}}{N_{i}^{F}}}{\frac{\beta_{i}^{FwM}}{{\beta^{MwF}\frac{G_{i}^{MF}}{G^{M}}} + N_{i}^{F}}} = {\frac{\beta_{i}^{FwoM}}{\beta_{i}^{FwM}}\left( {{\beta^{MwF}\frac{G_{i}^{MF}}{G^{M}N_{i}^{F}}} + 1} \right)}}}$${SR}^{M} = {\frac{{SINR}^{MwoF}}{{SINR}^{MwF}} = {\frac{\frac{\beta^{MwoF}}{N^{M}}}{\frac{\beta^{MwF}}{{\sum\limits_{i = 1}^{N_{f}}\; {\beta_{i}^{FwM}\frac{G_{i}^{FM}}{G_{i}^{F}}}} + N^{M}}} = {\frac{\beta^{MwoF}}{\beta^{MwF}}\left( {{\sum\limits_{i = 1}^{N_{f}}\; {\beta_{i}^{FwM}\frac{G_{i}^{FM}}{G_{i}^{F}N^{M}}}} + 1} \right)}}}$

where FwoM denotes at home base station HBS without interference ofinterfering mobile terminals MT served by base station BS, FwM denotesat home base station HBS with interference of interfering mobileterminals MT served by base station BS, MwoF denotes at base station BSwithout interference of interfering mobile terminals MT served by homebase stations HBS, MwF denotes at base station BS with interference ofinterfering mobile terminals MT served by home base stations HBS, N^(M)is the level of AWGN plus interference level from neighbouring cells CEof the cell of the base station BS at the base station BS, N_(i) ^(F) isthe level of AWGN plus interference from neighbouring cells CE of thecell of the base station BS in which the home base station HBS islocated at the home base station HBS, G_(i) ^(FM) is the path gainbetween a mobile terminal MT served by home base station HBSi and thebase station BS, G_(i) ^(MF) is the path gain between the home basestation HBSi and a mobile terminal MT served by base station BS. Notethat indices j and k are omitted here, since the optimisation processdoes not consider a mobile terminal MT in particular. Thus, path gainsare random variables.

For the optimisation, the mean degradation over all potential positionsof mobile terminals MT served by a base station BS and the meandegradation over all potential positions of mobile terminals MT servedby a home base station HBS are considered and the following equationshave to be solved:

${E\left\lbrack {SR}_{i}^{F} \right\rbrack} = {{E\left\lbrack \frac{{SINR}_{i}^{FwoM}}{{SINR}_{i}^{FwM}} \right\rbrack} = {{\frac{\beta_{i}^{FwoM}}{\beta_{i}^{FwM}}\left( {{\beta^{MwF}{E\left\lbrack \frac{G_{i}^{MF}}{G^{M}N_{i}^{F}} \right\rbrack}} + 1} \right)} = \delta}}$${E\left\lbrack {SR}^{M} \right\rbrack} = {{E\left\lbrack \frac{{SINR}^{MwoF}}{{SINR}^{MwF}} \right\rbrack} = {{\frac{\beta^{MwoF}}{\beta^{MwF}}\left( {{E\left\lbrack {\sum\limits_{i = 1}^{N_{f}}\; {\beta_{i}^{FwM}\frac{G_{i}^{FM}}{G_{i}^{F}N^{M}}}} \right\rbrack} + 1} \right)} = \delta}}$

where E X= X denotes the mean of variable X Different beta values arechosen with (β_(i) ^(FwM), β^(MwF)) and without interference (β_(i)^(FwoM), β^(MwoF)). For instance, the (β_(i) ^(FwoM), β^(MwoF)) valueswithout interference are already known.

After analytical system derivation, we obtain the following solution,

$\beta^{MwF} = {\beta^{MwoF}\frac{1 + {\frac{1}{{}_{\;}^{}{N\_}_{\;}^{}}{\sum\limits_{i^{\prime} = 1}^{N_{f}}\; {\beta_{i}^{FwoM}{\overset{\_}{z}}_{i^{\prime}}^{F}}}}}{\delta - {\frac{\beta^{MwoF}}{\delta {{}_{\;}^{}{N\_}_{\;}^{}}}{\sum\limits_{i^{\prime} = 1}^{N_{f}}\; {\beta_{i}^{FwoM}\frac{{\overset{\_}{z}}_{i}^{M}{\overset{\_}{z}}_{i^{\prime}}^{F}}{{}_{\;}^{}{N\_}_{}^{}}}}}}}$$\beta_{i}^{FwM} = {\frac{\beta_{i}^{FwoM}}{\delta}\left( {{\frac{{\overset{\_}{z}}_{i}^{M}}{{}_{\;}^{}{N\_}_{}^{}}\beta^{MwoF}\frac{1 + {\frac{1}{{}_{\;}^{}{N\_}_{\;}^{}}{\sum\limits_{i^{\prime} = 1}^{N_{f}}\; {\beta_{i}^{FwoM}{\overset{\_}{z}}_{i^{\prime}}^{F}}}}}{\delta - {\frac{\beta^{MwoF}}{\delta {{}_{\;}^{}{N\_}_{\;}^{}}}{\sum\limits_{i^{\prime} = 1}^{N_{f}}\; {\beta_{i}^{FwoM}\frac{{\overset{\_}{z}}_{i}^{M}{\overset{\_}{z}}_{i^{\prime}}^{F}}{{}_{\;}^{}{N\_}_{}^{}}}}}}} + 1} \right)}$${{{where}\mspace{14mu} {\overset{\_}{z}}_{i}^{M}} = {E\left\lbrack \frac{G_{i}^{MF}}{G^{M}} \right\rbrack}},{{{}_{\;}^{}{N\_}_{\;}^{}} = \frac{1}{E\left\lbrack \frac{1}{N^{M}} \right\rbrack}},{{\overset{\_}{z}}_{i}^{F} = {{{E\left\lbrack \frac{G_{i}^{FM}}{G_{i}^{F}} \right\rbrack}\mspace{14mu} {and}\mspace{14mu} {{}_{\;}^{}{N\_}_{}^{}}} = {\frac{1}{E\left\lbrack \frac{1}{N_{i}^{F}} \right\rbrack}.}}}$

Alternatively, the (β_(i) ^(FwoM), β^(MwoF)) values without interferenceare not already known, they may be determined also by the base stationBS or by the server Serv.

For instance, the (β_(i) ^(FwoM), β^(MwoF)) values without interferencecan be chosen such that each home base station HBS cell has the sameaverage SINR and that the base station BS the cell of which comprisesthe home base stations HBS has a given mean SINR:

$\beta^{MwF} = {\alpha^{M}\mspace{14mu} {{}_{\;}^{}{N\_}_{\;}^{}}\frac{1 + {\frac{\alpha^{F}}{{}_{\;}^{}{N\_}_{\;}^{}}{\sum\limits_{i^{\prime} = 1}^{N_{f}}\; {{{}_{\;}^{}{N\_}_{i\prime}^{}}{\overset{\_}{z}}_{i^{\prime}}^{F}}}}}{\delta - {\frac{\alpha^{M}\alpha^{F}}{\delta}{\sum\limits_{i^{\prime} = 1}^{N_{f}}\; {{\overset{\_}{z}}_{i}^{F}{\overset{\_}{z}}_{i^{\prime}}^{F}}}}}}$$\beta_{i}^{FwM} = {\frac{\alpha^{F}\mspace{14mu} {{}_{\;}^{}{N\_}_{}^{}}}{\delta}\left( {{\frac{{\overset{\_}{z}}_{i}^{M}\alpha^{M}\mspace{14mu} {{}_{\;}^{}{N\_}_{\;}^{}}}{{}_{\;}^{}{N\_}_{}^{}}\frac{1 + {\frac{\alpha^{F}}{{}_{\;}^{}{N\_}_{\;}^{}}{\sum\limits_{i^{\prime} = 1}^{N_{f}}\; {{{}_{\;}^{}{N\_}_{i\prime}^{}}{\overset{\_}{z}}_{i^{\prime}}^{F}}}}}{\delta - {\frac{\alpha^{M}\alpha^{F}}{\delta}{\sum\limits_{i^{\prime} = 1}^{N_{f}}\; {{\overset{\_}{z}}_{i}^{M}{\overset{\_}{z}}_{i^{\prime}}^{F}}}}}} + 1} \right)}$

where α^(F) is the target SINR of all mobile terminals MT served by homebase stations HBS and α^(M) is the target SINR of all mobile terminalsMT served by the base station BS the cell CE of which comprises the homebase stations HBS.

The expressions of optimum β values β_(i) ^(FwM) depend on twostatistics for each home base station HBS received at step S600 and1+N_(f) statistics obtained at step S601 for one base station BS thecell CE of which comprises the home base stations HBS, where N_(f) isthe number of home base stations HBS in the cell CE of the base stationBS.

The statistics flows from a base station BS to the server Serv when thepresent algorithm is executed by the server Serv, comprise the mean overall mobile terminals currently or previously served by the base stationBS of path gain ratios i.e. the path gain between mobile terminal MT andhome base station HBSi over the path gain between mobile terminal MT andbase station BS for each interfered home base station HBSi

${\overset{\_}{z}}_{i}^{M} = {E\left\lbrack \frac{G_{i}^{MF}}{G^{M}} \right\rbrack}$

where G^(M) denotes the path gain between a mobile terminal MT served bya base station BS and the base station BS and G_(i) ^(MF) denotes thepath gain between a mobile terminal MT served by a base station BS andthe home base station HBSi located in the cell CE of the base stationBS. The statistic flows comprise also the harmonic mean of noise AWGNplus interference level, on base station BS

${{}_{\;}^{}{N\_}_{\;}^{}} = {\frac{1}{E\left\lbrack \frac{1}{N^{M}} \right\rbrack}.}$

The statistics flows from a home base station HBS to the server Serv arewhen the present algorithm is executed by the server Serv or thestatistics flows from a home base station HBS to the base station BS arewhen the present algorithm is executed by the base station BS, the meanover all mobile terminals MT served by the home base station HBS of pathgain ratios, i.e. the path gain between a mobile terminal MT served by ahome base station HBS and the base station BS over the path gain betweenthe mobile terminal MT served by a home base station HBS and the homebase station HBS for each home base station HBSi,

${{\overset{\_}{z}}_{i}^{F} = {E\left\lbrack \frac{G_{i}^{FM}}{G_{i}^{F}} \right\rbrack}},$

and are the harmonic mean of noise on the home base station HBSi locatedin the cell CE of the base station BS

${{}_{\;}^{}{N\_}_{}^{}} = \frac{1}{E\left\lbrack \frac{1}{N_{i}^{F}} \right\rbrack}$

Each home base station HBS sends two values. The base station BS sendsN_(f)+1 values to the server Serv when the present algorithm is executedby the server Serv.

The server Serv or the base station BS processes the statistics andoutputs one optimum β value for each home base station HBS and oneoptimum β value for the base station BS.

According to a second example of realization of the present invention,the power setting at the base station BS is already set and a globalpower setting for the home base stations HBS located in the cell of thebase station BS needs to be determined.

The function f is common to all the home base stations HBS located inthe cell CE of the base station BS. The considered power control invertsthe interference path gain,

${f\mspace{14mu} G^{I}} = {\frac{\beta}{G^{I}}.}$

where G^(I) is the interference path gain. The resulting power controlwith this function is for all the home base stations HBS located in thecell of the base station BS

$P_{i,j}^{F} = {{f^{F}\mspace{14mu} G_{i,j}^{FM}} = \frac{\beta^{F}}{G_{i,j}^{FM}}}$

where P_(i,j) ^(F) is the transmit power for a mobile terminal MTjserved by a home base station HBSi and G_(i,j) ^(FM) is the interferencepath gain between the mobile terminal MTj served by the home basestation HBSi and the base station BS.

The degradation on base station BS due to mobile terminals served byhome base stations HBS is for example set on a given level. Thedegradation on base station BS is defined by the ratio a of meaninterference level on base station BS due to mobile terminals MT servedby home base stations HBS in the cell CE of the base station BS overmean of AWGN plus interference level on base station BS without theinterference due to mobile terminals MT served by home base stations HBSN^(M).

If we consider a home base station HBS load of ρ_(i) for home basestation HBSi, the total interference I^(FM) from all mobile terminalsserved by the home base stations HBS at the base station BS is,

$I^{FM} = {{E\left\lbrack {\sum\limits_{i = 1}^{N_{f}}\; {a_{i}\frac{\beta^{F}}{G_{i,j}^{FM}}G_{i,j}^{FM}}} \right\rbrack} = {\alpha \; {E\left\lbrack N^{M} \right\rbrack}}}$

where a_(i) is the indicator of activity which is equal to 0 withprobability 1-ρ_(i) and 1 with probability ρ_(i). The load of a basestation BS or a home base station HBS is the probability that theresource is used, that is the probability that the activity indicator isequal to one.

The load of a base station BS or of a home base station HBS is linked toa percentage of resources used by the home base station HBS in its cellCEHB. The percentage of resources is preferably a mean over a given timeperiod or is a probability of an amount of resources used by the homebase station HBS in its cell CEHB. An indicator of activity equal to 1means that the resource is used.

After analytical resolution, the global power parameter β^(F) is equalto

$\beta^{F} = {\frac{\alpha \; {\overset{\_}{N}}^{M}}{\sum\limits_{i = 1}^{N_{f}}\; \rho_{i}} \leq \frac{\alpha \; {\overset{\_}{N}}^{M}}{N_{f}}}$

where N ^(M)=E[N^(M)]. If we consider full load (ρ_(i)=1, ∀i),

$\beta^{F} = {\frac{\alpha \; {\overset{\_}{N}}^{M}}{N_{f}}.}$

The expression of the optimum β^(F) value depends on mean noise andpossibly on home base stations HBS load.

The statistics flows from a base station BS to the server Serv comprisewhen the present algorithm is executed by the server Serv, the mean ofnoise on base station BS N ^(M)=E[N^(M)].

The statistics flows from a home base station BS to the server Serv maycomprise when the present algorithm is executed by the server Serv orthe statistics flows from a home base station HBS to the base station BSmay comprise when the present algorithm is executed by the base stationBS, the load of the home base station HBS if it is not estimated by theserver Serv or the base station BS based on wired backhaul load.

According to a third example of realization of the present invention,the power setting at the base station BS is already set and a globalpower setting for the home base stations HBS located in the cell of thebase station BS needs to be determined.

Unlike the second example of realization, there is no more a prioristructure of the function f.

The function f is common to all home base stations HBS. The structure isa priori free and depends on the path gain between mobile terminals MTserved by home base stations HBS and base stations BS.

The degradation α on base station BS due to mobile terminals MT servedby home base stations HBS is set on a given level and the home basestations HBS performance level is maximised.

The law of random variables is considered with a quantified probabilitydensity function (pdf)

$G_{n_{bin}}^{FM};{\Pr_{n_{{bin}_{n_{{bin} = {1\cdots \; N_{bin}}}}}}^{I}.}$

$G_{n_{bin}}^{FM};\Pr_{n_{{bin}_{n_{{bin} = {1\cdots \; N_{bin}}}}}}^{I}$

describes the law of path gains between mobile terminals MT served by ahome base station HBS and base station BS irrespective of the home basestation HBS. G_(n) _(bin) ^(FM) represents a range of interference pathgain and Pr_(n) _(bin) ^(I) is the probability of the range. We search avector {circumflex over (P)}^(F) which corresponds to a maximum of

$\rho \; N_{f}{\sum\limits_{n_{bin} = 1}^{N_{bin}}\; {\Pr_{n_{bin}}^{I}\mspace{14mu} C\mspace{14mu} P_{n_{bin}}^{F}}}$

and satisfies the constraint

${\rho \; N_{f}{\sum\limits_{n_{bin} = 1}^{N_{bin}}\; {G_{n_{bin}}^{FM}\Pr_{n_{bin}}^{I}P_{n_{bin}}^{F}}}} = {\alpha \; {E\left\lbrack N^{M} \right\rbrack}\text{:}}$${\hat{P}}^{F} = {\arg \mspace{14mu} {\max\limits_{{P^{F}|{\rho \; N_{f}{\sum\limits_{n_{bin} = 1}^{N_{bin}}\; {G_{n_{bin}}^{FM}\Pr_{n_{bin}}^{I}P_{n_{bin}}^{F}}}}} = {\alpha \; {E{\lbrack N^{M}\rbrack}}}}\left( {\rho \; N_{f}{\sum\limits_{n_{bin} = 1}^{N_{bin}}\; {\Pr_{n_{bin}}^{I}\mspace{14mu} C\mspace{14mu} P_{n_{bin}}^{F}}}} \right)}}$

where, P^(F)=[P₁ ^(F), P₂ ^(F), . . . , P_(N) _(bin) ^(F)], P_(n) _(bin)^(F) is the common transmit power solution corresponding to the pathgain G_(n) _(bin) ^(FM) and ρ is a constant load over all home basestations.

$\hat{Z} = {\arg \mspace{14mu} {\max\limits_{Z|{constraint}}\mspace{14mu} {F\mspace{14mu} Z}}}$

denotes a value {circumflex over (Z)} of Z which corresponds to amaximum value of the function F Z and satisfies the constraintconstraint. Alternatively, if the load is different among home basestations HBS, the load of each home base station HBS is included in

$G_{n_{bin}}^{FM};{\Pr_{n_{{bin}_{n_{bin} = {1\cdots \; N_{bin}}}}}^{I}.}$

The function C P is the performance metric where P is the transmitpower. For instance, C P is approximately equal to log₂ 1+γP, which is ahome base station HBS Shannon capacity bound on mean performance overall home base stations HBS performances if γ is the mean ratio over thehome base stations HBS of the path gain between mobile terminals MTserved by a home base station HBS and the home base station HBS and AWGNplus interference level received on home base station HBS which may becommon to all home base stations HBS.

C P may be a home base station HBS Shannon capacity bound on a cell-edgeperformance if γ is a quantile of the ratio of the path gain betweenmobile terminals MT served by a home base station HBS and the home basestation HBS and AWGN plus interference level received on home basestation HBS common to all home base stations HBS.

A quantile u_(Q)=Q_(u)(P) is the value u_(Q) of u such that theprobability that u is lower than u_(Q) is equal to P.

γ is considered as a constant value for all the home base stations HBS,e.g., the mean of ratio of path gain between mobile terminals MT servedby a home base station HBS and the home base station HBS and AWGN plusinterference level received on home base station HBS.

After analytical optimisation:

$P^{F} = {{f\mspace{14mu} G^{FM}} = {\frac{1}{\gamma}\left( {\frac{\frac{{\gamma\alpha}\; {\overset{\_}{N}}^{M}}{\rho \; N_{f}} + {\overset{\_}{G}}^{FM}}{G^{FM}} - 1} \right)}}$

where G ^(FM)=E[G^(FM)] is the mean over all home base stations HBS ofinterference path gain between a mobile terminal MT served by a homebase station HBS and the base station BS. The γ value can be chosenarbitrarily or set in order to limit the occurrences of zero transmitpower.

After maximisation, the mean performance metric C_(mean) over all homebase stations HBS is

${C_{mean} = {\rho \left( {\log \left( {\frac{{\gamma\alpha}\; {\overset{\_}{N}}^{M}}{\rho \; N_{f} \times {{}_{\;}^{}{G\_}_{\;}^{}}} + \frac{{\overset{\_}{G}}^{FM}}{{}_{\;}^{}{G\_}_{\;}^{}}} \right)} \right)}},$

where ^(G) G ^(FM) is the geometrical mean,

${{}_{\;}^{}{G\_}_{\;}^{}} = {10^{\overset{\_}{\log_{10}{(G^{FM})}}}.}$

Another way of performing appropriate power control, instead ofmaximising C_(mean) for a given home base station HBS degradation α, isto minimize the base station BS degradation α for a given meanperformance metric C_(mean).

P^(F) equation only involves parameters common to all home base stationsHBS, except G^(FM). In order to make the function f available to allhome base stations HBS, the two following parameters are broadcasted:

$\beta_{1}^{F} = \frac{1}{\gamma}$$\beta_{2}^{F} = {\frac{{\gamma\alpha}\; {\overset{\_}{N}}^{M}}{\rho \; {\overset{\_}{N}}_{f}} + {\overset{\_}{G}}^{FM}}$

According to P^(F) equation, the function f is

${f\mspace{14mu} G^{FM}} = {\beta_{1}^{F}\left( {\frac{\beta_{2}^{F}}{G^{FM}} - 1} \right)}$

Thus,

$P_{i,j}^{F} = {{\beta_{1}^{F}\left( {\frac{\beta_{2}^{F}}{G_{i,j}^{FM}} - 1} \right)}.}$

The expression of optimum β₁ ^(F) and β₂ ^(F) values depends on meannoise, mean of mobile terminals served by home base station HBS to basestation BS interference path gain and load of each home base stationHBS.

The statistics flows from a base station BS to the server Serv comprisewhen the present algorithm is executed by the server Serv, the mean ofnoise on base station BS N ^(M)=E[N^(M)].

The statistics flows from a home base station BS to the server Serv arewhen the present algorithm is executed by the server Serv or thestatistics flows from a home base station HBS to the base station BS arewhen the present algorithm is executed by the base station BS, the meanof mobile terminal MT served by a home base station to base station BSinterference path gain G _(i) ^(FM)=E[G_(i) ^(FM)] and may comprise theload of the home base station. At the server Serv or base station BS, G^(FM) is obtained from plural G _(i) ^(FM). For example, G ^(FM) is themean of plural G _(i) ^(FM).

These statistics are transferred to the server Serv or to the basestation BS. Each home base station HBS sends one or two values to theserver Serv or to the base station BS. The base station BS sends onevalue to the server Serv if the server Serv executes the presentalgorithm. The server Serv or the base station BS processes thestatistics and outputs two beta values β₁ ^(F) and β₂ ^(F) for all thehome base stations HBS.

According to a variant of the third example of realization of thepresent invention, the power setting at the base station BS is alreadyset and a global power setting for the home base stations HBS located inthe cell of the base station BS needs to be determined.

The function f which optimizes a given criterion is also searched.

The function f is common to all home base stations HBS. The structure isa priori free and depends on the interference and useful path gains.

The degradation α on base station BS due to home base stations HBS isset on a given level and the home base stations HBS performance level ismaximised.

The laws of random variables are

$G_{n_{bin}}^{FM};\Pr_{n_{{bin}_{n_{bin} = {1\cdots \; N_{bin}}}}}^{I}$

for the path gain between a mobile terminal MT served by a home basestation HBS and a base station BS and

$y_{m_{bin}};\Pr_{m_{{bin}_{m_{bin} = {1\cdots \; M_{bin}}}}}^{U}$

for the path gain between a mobile terminal MT served by a home basestation HBS and the home base station HBS or the ratio of this path gainover the AWGN plus interference level received at home base station HBS.

$G_{n_{bin}}^{FM};{\Pr_{n_{{bin}_{n_{bin} = {1\cdots \; N_{bin}}}}}^{I}\mspace{14mu} {and}\mspace{14mu} y_{m_{bin}}};\Pr_{m_{{bin}_{m_{bin} = {1\cdots \; M_{bin}}}}}^{U}$

describe the laws for all home base stations. In other words, the lawsare irrespective of the home base station HBS.

The path gain or the ratio of path gain over the AWGN plus interferencelevel may be replaced by any parameter representing the link qualitybetween a mobile terminal MT served by a home base station HBS and abase station BS or a mobile terminal MT served by a home base stationHBS and the home base station HBS. We consider,

${\hat{P}}^{F} = {\arg \mspace{14mu} {\max\limits_{{P^{F}|{\rho \; N_{f}{\sum\limits_{n_{bin} = 1}^{N_{bin}}\; {G_{n_{bin}}^{FM}\Pr_{n_{bin}}^{I}P_{n_{bin}}^{F}}}}} = {\alpha \; {E{\lbrack N^{M}\rbrack}}}}({Val})}}$${where},{{Val} = \left( {\rho \; N_{f}{\sum\limits_{m_{bin} = 1}^{N_{bin}}\; {\sum\limits_{n_{bin} = 1}^{N_{bin}}\; {\Pr_{m_{bin}}^{U}\Pr_{n_{bin}}^{I}C\mspace{14mu} P_{n_{bin}}^{F}y_{m_{bin}}}}}} \right)},P_{n_{bin},m_{bin}}^{F}$

is the common transmit power solution corresponding to the path gainG_(n) _(bin) ^(FM) and the path gain y_(m) _(bin) .

The function C P, y is the performance metric, where y is the path gainbetween a mobile terminal MT served by a home base station HBS and thehome base station HBS or the ratio of path gain between a mobileterminal MT served by a home base station HBS and the home base stationHBS over the AWGN plus interference level at home base station HBS.

For instance, C P, y is approximately equal to log₂ 1+γyP, which is ahome base station HBS Shannon capacity bound on performance if y is thepath gain between a mobile terminal MT served by a home base station HBSand the home base station HBS and γ is the mean over all home basestation cells of the inverse of

AWGN plus interference level received on home base stations HBS which iscommon to all home base stations HBS.

For instance, C P, y is approximately equal to log₂ 1+γyP, which is ahome base station HBS Shannon capacity bound on performance if y is theratio of the path gain between a mobile terminal MT served by a homebase station HBS and the home base station HBS over the AWGN plusinterference level and γ is a constant.

For instance, C P, y is approximately equal to log₂ 1+γyP, which is ahome base station HBS Shannon capacity bound on a cell-edge performanceif y is the path gain between a mobile terminal MT served by a home basestation HBS and the base station HBS and γ is a quantile of the inverseof AWGN plus interference level received on home base station HBS commonto all home base stations HBS.

γ is considered as a constant value for all the home base stations HBS,e.g., the mean of the inverse of AWGN plus interference level receivedon home base stations HBS if y is the path gain between a mobileterminal MT served by a home base station HBS and the home base stationHBS.

After analytical optimisation :

${P^{F} = {f\mspace{14mu} G^{FM}}},{y = {{\frac{1}{\gamma}\left( {\frac{\frac{{\gamma\alpha}\; {\overset{\_}{N}}^{M}}{\rho \; N_{f}} + \overset{\_}{z}}{G^{FM}} - \frac{1}{y}} \right)\mspace{14mu} {where}\mspace{14mu} \overset{\_}{z}} = {{{E\left\lbrack \frac{G^{FM}}{y} \right\rbrack} \approx {{E\left\lbrack G^{FM} \right\rbrack} \times {E\left\lbrack \frac{1}{y} \right\rbrack}}} = \frac{{\overset{\_}{G}}^{FM}}{H_{\overset{\_}{y}}}}}}$

is the mean over all the home base stations HBS of ratio of the pathgain between the mobile terminals MT served by a home base station HBSand the base station BS G^(FM) over the path gain y between the mobileterminals MT served by a home base station HBS and the home base stationHBS. If y is path gain between the mobile terminals MT served by a homebase station HBS and the home base station HBS,

$\overset{\_}{z} = \frac{{\overset{\_}{G}}^{FM}}{{}_{\;}^{}{G\_}_{\;}^{}}$

or if y is the ratio of the path gain between the mobile terminals MTserved by a home base station HBS and the home base station HBS over theAWGN plus interference level at home base station HBS,

$\overset{\_}{z} = {\frac{{\overset{\_}{G}}^{FM}{\overset{\_}{N}}^{F}}{{}_{\;}^{}{G\_}_{\;}^{}}.}$

^(H) x denotes the harmonic mean of x.

The global means G ^(FM), ^(H) G ^(F) and N ^(F) can be computed at thebase station BS or by the server Serv based on individual means for eachhome base station HBS,

${\overset{\_}{G}}^{FM} = {\sum\limits_{i = 1}^{N_{f}}\; {\rho_{i}{\overset{\_}{G}}_{i}^{FM}}}$${{}_{\;}^{}{G\_}_{\;}^{}} = \frac{1}{\sum\limits_{i = 1}^{N_{f}}\; {\rho_{i}\frac{1}{{}_{\;}^{}{G\_}_{}^{}}}}$${\overset{\_}{N}}^{F} = {\sum\limits_{i = 1}^{N_{f}}\; {\rho_{i}{\overset{\_}{N}}_{i}^{F}}}$

where N_(i) ^(F) is the level of AWGN plus interference fromneighbouring cells CE of the cell of the base station BS where the homebase station HBS is located and from the base station BS at the homebase station HBS.

The γ value can be chosen arbitrarily or set in order to limit theoccurrences of zero transmit power due to the subtraction in theequation defining P^(F).

The mean performance metric C_(mean) over all home base stations HBS is,

${C_{mean} = {N\mspace{14mu} {\log\left( \frac{{\gamma \frac{\alpha \; {\overset{\_}{N}}^{M}}{\rho \; {\overset{\_}{N}}_{f}}} + \overset{\_}{z}}{G_{\overset{\_}{z}}} \right)}}},$

where

$G_{\overset{\_}{z} = 10}^{\overset{\_}{\log_{10}{(\frac{G^{FM}}{G^{F}})}}}$

if y is the path gain between the mobile terminals MT served by a homebase station HBS and the home base station HBS, or

$G_{\overset{\_}{z} = 10}^{\overset{\_}{\log_{10}{(\frac{G^{FM}N^{F}}{G^{F}})}}}$

if y is the ratio of the path gain between the mobile terminals MTserved by a home base station HBS and the home base station HBS over theAWGN plus interference level at home base station HBS.

Another way of performing appropriate power control, instead ofmaximising C_(mean) for a given base station BS degradation α, is tominimize the base station BS degradation α for a given mean performancemetric C_(mean).

The equation defining P^(F) only involves parameters common to all homebase stations HBS, except G^(FM) and y. Thus, in order to make thefunction f available to all home base stations, the two followingparameters are broadcasted:

$\beta_{1}^{F} = \frac{1}{\gamma}$$\beta_{2}^{F} = {\frac{{\gamma\alpha}\; {\overset{\_}{N}}^{M}}{\rho \; {\overset{\_}{N}}_{f}} + \overset{\_}{z}}$

According to the equation defining P^(F), the function f is

${f\mspace{14mu} G^{1}} = {\beta_{1}^{F}\left( {\frac{\beta_{2}^{F}}{G^{1}} - \frac{1}{y}} \right)}$

So,

$P_{i,j}^{F} = {{\beta_{i}^{F}\left( {\frac{\beta_{2}^{F}}{G_{i,j}^{FM}} - \frac{1}{y_{i,j}}} \right)}.}$

The statistics flows from a base station BS to the server Serv comprisewhen the present algorithm is executed by the server Serv, the mean ofnoise on base station BS N ^(M)=E[N^(M)].

The statistics flows from a home base station BS to the server Serv whenthe present algorithm is executed by the server Serv or the statisticsflows from a home base station HBS to the base station BS when thepresent algorithm is executed by the by the base station BS comprise themean of the path gain between mobile terminal MT served by a home basestation HBS and the base station BS G _(i) ^(FM)=E[G₁ ^(FM)], theharmonic mean of the path gain between mobile terminal MT served by ahome base station HBS and the home base station HBS ^(H) G _(i)^(F)=1/E[1/G_(i) ^(F)], and the mean of the noise on home base stationHBS N _(i) ^(F)=E[N_(i) ^(F)] and may comprise the home base station HBSload.

According to a fourth example of realization of the present invention,the power setting is determined according to a numerical optimization.

Unlike the analytical approach, as disclosed in the above mentionedexample, the server Ser or the base station BS processes a numericaloptimization. The numerical approach allows to take into account moreprecise performance metrics like spectral efficiency with saturation,scheduling effects, outage or mean spectral efficiency and isparticularly suited to look-up tables LUTs linking for examplemiddle-scale SINR and metric performance. The numerical approximationmay be advantageous in order to consider other statistics for globalperformance on all home base stations HBS, e.g., quantile of meanmetrics performances, quantile of quantile metrics performances, globalquantiles, . . . .

For example, the function f is defined according to a vector β_(v),stored in a LUT which may contain all possible values for path gains andcorresponding transmit power:

{P_(m, n)^(F), S_(m)^(G^(F)), S_(n)^(G^(FM))}_(m = 1⋯ N_(i)^(G^(F)), n = 1⋯ N^(G^(FM))).S_(m)^(G^(F)) = [G_(m)^(F−), G_(m)^(F+)[, m = 1⋯ N^(G^(F))S_(n)^(G^(FM)) = [G_(n)^(FM−), G_(n)^(FM+)[, n = 1⋯ N^(G^(FM))

where P_(m,n) ^(F) is the transmit power corresponding to a G^(F) whichis comprised in [G_(m) ^(F−), G_(m) ^(F+)[ and represented by scalarvalue S_(m) ^(G) ^(F) and corresponding to a G^(FM) which is comprisedin [G_(n) ^(FM−), G_(n) ^(FM+)[ and represented by scalar value S_(n)^(G) ^(FM) .

Thus, we have (N^(G) ^(F) +N^(G) ^(FM) )+N^(G) ^(F)N^(G) ^(FM) scalarparameters in the β_(v) vector. The relation f is described by,

$n^{\prime} = {\sum\limits_{n = 1}^{N^{G^{FM}}}\; {n \times 1_{G^{FM} \in {\lbrack{G_{n}^{{FM} -},{G_{n}^{{FM} +}\lbrack}}}}}}$$m^{\prime} = {\sum\limits_{n = 1}^{N^{G^{F}}}\; {m \times 1_{G^{F} \in {\lbrack{G_{m}^{F -},{G_{m}^{F +}\lbrack}}}}}}$P^(F) = P_(m^(′), n^(′))^(F)

or more simply m′ and n′ are chosen as the indices of S_(m′) ^(G) ^(F)and S_(n′) ^(G) ^(FM) which are the nearest to G^(F) and G^(FM),respectively. 1_(x∈χ) equals 1 if x∈χ and 0 otherwise. In the following,P^(F) G^(F), G^(FM)=P_(m′,n′) ^(F).

In a variant, P^(F) G^(F), G^(FM) may be determined from interpolationwith P^(F) values corresponding to several m′ and n′.

As in previous examples,

$P^{F} = {\arg \mspace{14mu} \begin{matrix}\max\limits_{P^{F}|{{E{\lbrack{{\sum\limits_{i = 1}^{N_{f}}\; {\Delta_{i}G_{i}^{FM}P_{i}^{F}C_{i}^{FM}}},G_{i}^{F}}\rbrack}} - {\alpha \; {E{\lbrack N^{M}\rbrack}}}}} \\{Q_{\sum\limits_{i = 1}^{N_{f}}\; {a_{i}Q_{{{CP}_{i}^{F}G_{i}^{FM}},G_{i}^{F},G_{i}^{F},N_{i}^{F}}P_{out}}}\left( P_{out} \right)}\end{matrix}}$

A quantile u_(Q)=Q_(u)(P_(out)) is the value u_(Q) of u such that theprobability that u is lower than u_(Q) is equal to P_(out). For example,P_(out)=5%.

Instead of two quantiles in the above formula, a mean and a quantile maybe also chosen, or a single global quantile may also be chosen.

Instead of having a being the ratio of means, α may be the mean of theratio

${\frac{1}{N^{M}}{\sum\limits_{i = 1}^{N_{f}}\; {a_{i}G_{i}^{FM}P_{i}^{F}G_{i}^{FM}}}},$

G_(i) ^(F) or a quantile of this ratio.

In the above formula, several random variables appear. The activityvariable a_(i), the path gain G_(i) ^(FM) between a mobile terminal MTserved by a home base station HBSi and the base station BS, the pathgain G_(i) ^(F) between a mobile terminal MT served by the home basestation HBSi and the home base station HBSi and the AWGN plusinterference level at the home base station HBSi N_(i) ^(F). N_(i) ^(F)is the level of AWGN plus interference from neighbouring cells CE of thecell of the base station BS where the home base station HBS is locatedand from the base station BS at the home base station HBS.

The independency between home base stations HBS and between thedifferent variables may be used. The probability law of G_(i) ^(F) maybe considered identical for all home base stations HBS. Considering theindependency, the constraint can be rewritten as

${E\left\lbrack {\sum\limits_{i = 1}^{N_{f}}\; {a_{i}G_{i}^{FM}P_{i}^{F}}} \right\rbrack} = {{\sum\limits_{i = 1}^{N_{f}}\; {\rho_{i}{E\left\lbrack {G_{i`}^{FM}P_{i}^{F}} \right\rbrack}}} = {\alpha \; {{E\left\lbrack N^{M} \right\rbrack}.}}}$

For example, the function f does not depend on base station BS and homebase stations HBS positions and environment, i.e., on a particulardeployment, and the same law is applicable to plural base stations. Theprobability law of G_(i) ^(FM) is common to all base stations BS andhome base stations HBS.

For example, the function f depends on base station BS and home basestations HBS positions and environment, i.e. on a particular deployment.The probability law of G_(i) ^(FM) is function of i, especially themean, and the variances are smaller than the previous example.

For example, all laws are considered log-normal and independent. Thenonly the mean and standard deviation of the variable in logarithm scaleare needed.

The optimization may consist in generating multiple scenarios G_(i)^(F), G_(i) ^(FM), N_(i) ^(F), N^(M) _(j), j=1, . . . , N_(s), based onspecified probability laws, which are for example log-normal, executingseveral iterations for each scenario of choosing a potential transmitpower vector P₁ ^(F), . . . , P_(N) _(f) ^(F) satisfying the constraint

${{E\left\lbrack {\sum\limits_{i = 1}^{N_{f}}\; {a_{i}G_{i}^{FM}P_{i}^{F}}} \right\rbrack} = {\alpha \; {E\left\lbrack N^{M} \right\rbrack}}},$

computing the capacity C P_(i) ^(F), G_(i) ^(F), N_(i) ^(F) of eachactive home base station HBS, building capacity statistics on allscenarios, comparing between present statistics and previous ones,defining the gradient of the transmit power vector β_(v) and keeping thetransmit power table that leads to the maximum criterion.

Optimum β_(v) depends on at least a part of the following statistics:

-   -   the statistics flows from a base station BS to the server Serv        comprise when the present algorithm is executed by the server        Serv, the mean of noise on base station BS N ^(M)=E[N^(M)],    -   the statistics flows from a home base station HBSi to the server        Serv when the present algorithm is executed by the server Serv        or the statistics flows from a home base station HBSi to the        base station BS when the present algorithm is executed by the        base station BS, comprise the mean of the path gain between a        mobile terminal MT served by the home base station HBSi and base        station BS G _(i) ^(FM)=E[G_(i) ^(FM)], the standard deviation        of the path gain between a mobile terminal MT served by the home        base station HBSi and base station BS σ_(G) _(i) _(FM) =√{square        root over (E[G_(i) ^(FM)− G _(i) ^(FM) ² ])}, the mean of the        path gain between a mobile terminal MT served by the home base        station HBSi and the home base station HBSi G _(i) ^(F)=E[G_(i)        ^(F)], the standard deviation of the path gain between a mobile        terminal MT served by the home base station HBSi and the home        base station HBSi σ_(G) _(i) _(F) =√{square root over (E[G_(i)        ^(F)− G _(i) ^(F) ² ])}, the mean of noise on the home base        station HBSi N _(i) ^(F)=E[N_(i) ^(F)]and may comprise the load        of the home base station HBSi.

According to a fifth example of realization of the present invention,the power setting is determined according to a numerical optimization ofonly one parameter of a function of two variables.

The function f has a structure as follows:

${f\mspace{14mu} G^{FM}},{G^{F} = {{\min\left( {\frac{\beta_{1}}{G^{FM}},{\frac{\beta_{1}}{\overset{\_}{\left( \frac{G^{FM}}{G^{F}} \right)}}\frac{\beta_{2}}{G^{F}}}} \right)} = {\frac{\beta_{1}}{G^{FM}}\min \mspace{14mu} 1}}},{\beta_{2}x}$$x = \frac{\frac{G^{FM}}{G^{F}}}{\overset{\_}{\left( \frac{G^{FM}}{G^{F}} \right)}}$

So, we have two scalar parameters in the β=β₁, β₂ vector.

Alternatively, the ratio of path gain between a mobile terminal MTserved by a home base station HBS and the home base station HBS overAWGN plus interference level at home base station HBS can be consideredinstead of only the path gain between the mobile terminal MT served bythe home base station HBS and the home base station HBS:

${f\mspace{14mu} G^{FM}},G^{F},{N^{F} = {{\min\left( {\frac{\beta_{1}}{G^{FM}},{\frac{\beta_{1}}{\overset{\_}{\left( \frac{G^{FM}}{y} \right)}}\frac{\beta_{2}}{y}}} \right)} = {\frac{\beta_{1}}{G^{FM}}\min \mspace{14mu} 1}}},{\beta_{2}x}$$x = \frac{\frac{G^{FM}}{y}}{\overset{\_}{\left( \frac{G^{FM}}{y} \right)}}$$y = \frac{G^{F}}{N^{F}}$

For a sufficiently large number of home base stations HBS, the value ofparameter β₂ remains approximately the same whatever the home basestations HBS locations with respect to base station BS, or shadowingrealizations.

As in the fourth example of realization, we want to solve,

${\hat{\beta}}_{1},{{\hat{\beta}}_{2} = {\arg \mspace{14mu} {\max\limits_{\beta_{1},{{\beta_{2}|{E{\lbrack{{\sum\limits_{i = 1}^{N_{f}}\; {a_{i}G_{i}^{FM}f\mspace{14mu} G^{FM}}},{G^{F};\beta_{1}},\beta_{2}}\rbrack}}} = {\alpha \; {E{\lbrack N^{M}\rbrack}}}}}{{Val}\; 2}}}}$${{Val}\; 2} = {Q_{\sum\limits_{i = 1}^{N_{f}}\; {a_{i}Q_{C{({{f\mspace{14mu} G_{i}^{FM}},{G_{i}^{F};\beta_{1}},\beta_{2},G_{i}^{F},N_{i}^{F}})}}P_{out}}}\left( P_{out} \right)}$

For example, P_(out)=5%. Instead of two quantiles in the above formula,a mean and a quantile can be selected, or a single global quantile onall possible links of all home base stations HBS. Instead of having abeing the ratio of means, α may be the mean of the ratio

${\frac{1}{N^{M}}{\sum\limits_{i = 1}^{N_{f}}\; {a_{i}G_{i}^{FM}P_{i}^{F}G_{i}^{FM}}}},$

G_(i) ^(F) or a quantile of the ratio.

In the above formula, several random variables appear. The activitya_(i) of a home base station HBSi, the path gain G_(i) ^(FM) between amobile terminal MT served by the home base station HBS_(i) and the basestation BS, the path gain G_(i) ^(F) between a mobile terminal MT servedby the home base station HBSi and the home base station HBSi and theAWGN plus interference level at the home base station HBSi N_(i) ^(F).

The independency between home base stations HBS and between thedifferent variables may be used. In that case, the probability law ofG_(i) ^(F) can be consider identical for all home base stations HBS.

For example, if we consider the independency, the constraint can berewritten as

${E\left\lbrack {\sum\limits_{i = 1}^{N_{f}}\; {a_{i}G_{i}^{FM}P_{i}^{F}}} \right\rbrack} = {{\sum\limits_{i = 1}^{N_{f}}\; {\rho_{i}{E\left\lbrack {G_{i}^{FM}P_{i}^{F}} \right\rbrack}}} = {\alpha \; {E\left\lbrack N^{M} \right\rbrack}}}$

If all laws are considered log-normal and independent, only mean andstandard deviation of the variable are needed.

The optimization can consist in generating multiple scenarios G_(i)^(F), G_(i) ^(FM), N_(i) ^(F), N^(M) _(j), j=1, . . . , N_(s), based onspecified probability laws, executing plural iterations and for eachscenario, choosing a potential couple of parameters β₁, β₂ satisfyingthe constraint

${{E\left\lbrack {\sum\limits_{i = 1}^{N_{f}}\; {a_{i}G_{i}^{FM}P_{i}^{F}}} \right\rbrack} = {\alpha \; {E\left\lbrack N^{M} \right\rbrack}}},$

computing capacity C f G_(i) ^(FM), G_(i) ^(F); β₁, β₂, G_(i) ^(F),N_(i) ^(F) for each home base station HBS, building capacity statisticson all scenarios, comparing between present statistics and previousones, defining the gradient of transmit power vector and keeping thecouple of parameters β₁, β₂ that leads to the maximum criterion.

It has to be noted here that, the most flexible approach is to randomlyand independently choose all potential couples of parameters.

In order to simplify the process, relationship between the twoparameters and the mean noise plus interference level on base station BSmay be used when the normalized path gain ratios x_(i) are independentbetween different home base stations HBS.

${\alpha \; {E\left\lbrack N^{M} \right\rbrack}} = {\beta_{1}{\sum\limits_{i = 1}^{N_{f}}\; {\rho_{i}\left( {1 - \underset{\underset{\Pr {({x < \frac{1}{\beta_{2}}})}}{}}{\int_{0}^{1\text{/}\beta_{2}}{{pdf}\mspace{14mu} x_{i}\ {x}}} + {\beta_{2}{\int_{0}^{1\text{/}\beta_{2}}{x_{i} \times {pdf}\mspace{14mu} x_{i}\ {x}}}}} \right)}}}$

So,

$\beta_{1} = \frac{\alpha \; {E\left\lbrack N^{M} \right\rbrack}}{\sum\limits_{i = 1}^{N_{f}}\; {\rho_{i}\left( {1 - \underset{\underset{\Pr {({x < \frac{1}{\beta_{2}}})}}{}}{\int_{0}^{1\text{/}\beta_{2}}{{pdf}\mspace{14mu} x_{i}\ {x}}} + {\beta_{2}{\int_{0}^{1\text{/}\beta_{2}}{x_{i} \times {pdf}\mspace{14mu} x_{i}\ {x}}}}} \right)}}$

If path gains are log-normal, x_(i) is also log-normal and it enablesthe use of erfc( ) complementary error function to compute the firstparameter function of the second parameter and the mean interferencelevel due to home base stations HBS on base stations.

Thus, only β₂ is to be optimized.

The statistics flows from a base station BS to the server Serv comprisewhen the present algorithm is executed by the server Serv, the mean ofnoise on base station BS N ^(M)=E[N^(M)].

If all laws are considered log-normal and independent, the statisticsflows from a home base station HBSi to the server Serv are when thepresent algorithm is executed by the server Serv or the statistics flowsfrom the home base station HBSi to the base station BS when the presentalgorithm is executed by the base station BS comprise the mean of thepath gain between a mobile terminal MT served by the home base stationHBSi and the base station BS G _(i) ^(FM)=E[G_(i) ^(FM)], the standarddeviation of the path gain between a mobile terminal MT served by thehome base stations HBSi and the base station BS σ_(G) _(i) _(FM)=√{square root over (E[G_(i) ^(FM)− G _(i) ^(FM) ² ])}, the mean of thepath gain between a mobile terminal MT served by the home base stationsHBSi and the home base station HBSi G _(i) ^(F)=E[G_(i) ^(F)], thestandard deviation of the path gain between a mobile terminal MT servedby the home base station HBSi and the home base station HBSi σ_(G) _(i)_(F) =√{square root over (E[G_(i) ^(F)− G _(i) ^(F) ² ])}, the mean ofnoise on the home base station HBSi and may comprise the load of thehome base station HBSi.

At step S603, the processor 200 commands the transfer of power controlinformation to each home base station HBS comprised in its cell CEthrough the wireless interface 205 or through the network interface 206.

According to the first example of realization, the processor 200commands the transfer of the coefficient β_(i) ^(F) to each home basestation HBSi comprised in its cell CE.

According to the second example of realization, the processor 200commands the transfer of the coefficient β^(F) to all home base stationsHBS comprised in its cell CE.

According to the third example of realization, the processor 200commands the transfer of the coefficients β₁ ^(F) and β₂ ^(F) to allhome base stations HBS comprised in its cell CE.

According to the variant of the third example of realization of thepresent invention, the processor 200 commands the transfer of thecoefficients β₁ ^(F) and β₂ ^(F) to all home base stations HBS comprisedin its cell CE.

According to the fourth example of realization, the processor 200commands the transfer of the at most (N^(G) ^(F) +N^(G) ^(FM) )+N^(G)^(F) N^(G) ^(FM) values, comprising N^(G) ^(F) discrete G^(F) values,N^(G) ^(FM) discrete G^(FM) values and N^(G) ^(F) N^(G) ^(FM) powervalues.

According to the fifth example of realization, the processor 200commands the transfer of the coefficients β₁ and β₂ to all home basestations HBS comprised in its cell CE.

It has to be noted here that if a part or the function f is unknown bybase stations or home base stations or mobile terminals, said part orthe function f is also transferred.

Alternatively, the processor 400 commands the transfer of power controlinformation to each base station BS the server Serv is in charge of andto each home base station HBS comprised in the cell of each base stationBS the server Serv is in charge of through the network interface 406.

According to the first example of realization, the processor 400commands the transfer of the coefficient β^(M) to each base station BSthe server Serv is in charge of and the transfer of the coefficientβ_(i) ^(F) to each home base station HBSi comprised in the cell of eachbase station BS the server Serv is in charge of.

According to the second example of realization, the processor 400commands the transfer of the coefficient β^(F) to all home base stationsHBS comprised in the cell of each base station BS the server Serv is incharge of.

According to the third example of realization, the processor 400commands the transfer of the coefficients β₁ ^(F) and β₂ ^(F) to allhome base stations HBS comprised in the cell of each base station BS theserver Serv is in charge of.

According to the variant of the third example of realization of thepresent invention, the processor 400 commands the transfer of thecoefficients β₁ ^(F) and β₂ ^(F) to all home base stations HBS comprisedin the cell of each base station BS the server Serv is in charge of.

According to the fourth example of realization, the processor 400commands the transfer of the at most (N^(G) ^(F) +N^(G) ^(FM) )+N^(G)^(F) N^(G) ^(FM) values, comprising N^(G) ^(F) discrete G^(F) values,N^(G) ^(FM) discrete G^(FM) values and N^(G) ^(F) N^(G) ^(FM) powervalues to all home base stations HBS comprised in the cell of each basestation BS the server Serv is in charge of.

According to the fifth example of realization, the processor 400commands the transfer of the coefficients β₁ and β₂ to all home basestations HBS comprised in the cell of each base station BS the serverServ is in charge of.

After that, the processor 200 returns to step S600.

Alternatively, the processor 400 returns to step S600.

FIG. 7 discloses an algorithm executed by each home base station andeach base station according to the present invention.

More precisely, the present algorithm is executed by the processor 200of the base station BS and by the processor 300 of each home basestation HBS each time power control information is received.

At step S700, the processor 200 receives power control information asthe one transferred by the server Serv as disclosed at step S603 of thealgorithm of FIG. 6 or retrieves the power control information from theRAM memory 203.

At the same step, each processor 300 receives power control informationas the one transferred by the server Serv or the base station BS asdisclosed at step S603 of the algorithm of FIG. 6.

At next step S701, the processor 200 commands the transfer through thewireless interface 205, of the power control information to each mobileterminal MT served by the base station BS.

In a variant, the transmission power is transferred to each mobileterminal MT served by the base station BS.

At the same step, each processor 300 commands the transfer through thewireless interface 305, of the power control information to each mobileterminal MT served by the home base station HBS.

In a variant, the transmission power is transferred to each mobileterminal MT served by the home base station BS.

The processor 200 or 300 executes the step S701 as far as no powercontrol information is received.

Naturally, many modifications can be made to the embodiments of theinvention described above without departing from the scope of thepresent invention.

1-14. (canceled)
 15. A method for adjusting transmission power, in awireless cellular telecommunication network, of signals transferred byplural mobile terminals through a wireless interface, the mobileterminals being served by at least one base station or by home basestations, the home base stations being located in a cell of the at leastone base station, the method comprising: obtaining path gains betweenthe mobile terminals and the at least one base station and path gainsbetween the mobile terminals and at least one home base station, and/ornoise measured at the at least one base station and/or at the home basestations; determining statistics from the obtained path gains and/ornoise; obtaining at least one coefficient of a function according to atleast a part of the statistics determined from the obtained path gainsand/or noise; and transferring an information representative of the atleast one obtained coefficient to the mobile terminals to enable themobile terminals to transfer signals at a transmission power derivedfrom information representative of the at least one obtainedcoefficient.
 16. A method according to claim 15, wherein for mobileterminals served by the at least one base station, the path gainsbetween the mobile terminals and home base stations located in the cellof the at least one base station which serves the mobile terminals areobtained, and for mobile terminals served by home base stations, eachpath gain between a mobile terminal and only the home base stationserving the mobile terminal is obtained.
 17. A method according to claim15, wherein the function is defined for a continuous range of realvalues or a plurality of coefficients are obtained, the coefficientsbeing entries of a table representing the function.
 18. A methodaccording to claim 15, wherein each path gain is a path gain between onehome base station serving one mobile terminal and the mobile terminal,or the path gain between one base station serving one mobile terminaland the mobile terminal, or the path gain between one home base stationnot serving one mobile terminal and the mobile terminal, or the pathgain between one base station not serving one mobile terminal and themobile terminal.
 19. A method according to claim 15, wherein a set of atleast one coefficient of the function is determined for each home basestation and for the at least one base station.
 20. A method according toclaim 15, wherein a same set of at least one coefficient is determinedfor all the home base stations.
 21. A method according to claim 15,wherein the path gains are obtained by the home base stations and the atleast one base station and statistics are determined by the home basestations and the at least one base station.
 22. A method according toclaim 15, wherein the at least one coefficient of the function isobtained by the base station or by a server of the wireless cellulartelecommunication network.
 23. A method according to claim 15, whereininformation representative of the at least one obtained coefficient istransferred to each mobile terminal via the base station serving themobile terminal or via the home base station serving the mobileterminal.
 24. A method according to the claim 23, wherein when the atleast one coefficient of the function is obtained by the server, the atleast one base station transfers to the server the harmonic mean ofnoise measured at the at least one base station, and/or the mean ofnoise measured at the at least one base station, and/or the mean overall mobile terminals served or having been served by the at least onebase station of ratios of the path gain between a mobile terminal and ahome base station over the path gain between the mobile terminal and itsserving base station.
 25. A method according to the claim 23, whereineach home base station transfers to the base station in the cell ofwhich the home base station is located or to the server, the mean overall mobile terminals served or having been served by the home basestation of ratio of the path gain between a mobile terminal served by ahome base station and the base station over the path gain between themobile terminal served by a home base station and the home base station,and/or the harmonic mean of noise measured at the home base station,and/or the mean of the noise measured at the home base station, and/orthe mean over all mobile terminals served or having been served by thehome base station of the path gain between a mobile terminal served by ahome base station and the base station, and/or the standard deviationover all mobile terminals served or having been served by the home basestation of the path gain between a mobile terminal served by a home basestation and the base station, and/or the load of the home base station,and/or the harmonic mean over all mobile terminals served or having beenserved by the home base station of the path gain between a mobileterminal served by a home base station and the home base station, themean over all mobile terminals served or having been served by the homebase station of the path gain between a mobile terminal served by thehome base station and the home base station, and/or the standarddeviation over all mobile terminals served or having been served by thehome base station of the path gain between a mobile terminal served bythe home base station and the home base station.
 26. A system foradjusting the transmission power, in a wireless cellulartelecommunication network, of signals transferred by plural mobileterminals through a wireless interface, the mobile terminals beingserved by at least one base station or by home base stations, the homebase stations being located in the cell of the at least one basestation, the system comprising: means for obtaining path gains betweenthe mobile terminals and the at least one base station and path gainsbetween the mobile terminals and the home base stations, and/or noisemeasured at the at least one base station, and/or at the home basestations; means for determining statistics from the obtained path gainsand/or noise; means for obtaining at least one coefficient of a functionaccording to at least a part of the statistics determined from theobtained path gains and/or noise; and means for transferring aninformation representative of the at least one obtained coefficient tothe mobile terminals to enable the mobile terminals to transfer signalsat a transmission power derived from information representative of theat least one obtained coefficient.
 27. A system according to claim 26,wherein the means for obtaining the path gains are comprised in the homebase stations and the at least one base station and the means fordetermining statistics are comprised in the home base stations and theat least one base station.
 28. A system according to claim 26, whereinthe means for optimizing the at least one coefficient of the functionare comprised in the at least one base station or in a server of thewireless cellular telecommunication network.